Approximations in globally subanalytic and Denjoy-Carleman classes

Approximations in globally subanalytic and Denjoy-Carleman classes

Efroymson's Approximation Theorem asserts that if f is a C0 semialgebraic mapping on a C∞ semialgebraic submanifold M of Rn and if ε:M→R is a positive continuous semialgebraic function then there is a C∞ semialgebraic function g:M→R such that |f−g|

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2021-07, Vol.385, p.107764, Article 107764
Hauptverfasser: Valette, Anna, Valette, Guillaume
Format: Artikel
Sprache:eng
Schlagworte:
Analytic functions
Approximation theorem
Efroymson's theorem
Nash functions
o-minimal structures
Subanalytic functions
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Zusammenfassung:Efroymson's Approximation Theorem asserts that if f is a C0 semialgebraic mapping on a C∞ semialgebraic submanifold M of Rn and if ε:M→R is a positive continuous semialgebraic function then there is a C∞ semialgebraic function g:M→R such that |f−g|
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2021.107764